ParametricDerivative Command

ParametricDerivative( <Curve> )

Returns a new parametric curve given by \( \left( x(t), \frac{y'(t)}\{ x'(t)} \right) \).

ParametricDerivative(Curve(2t, t², t, 0, 10)) returns the parametric curve (x(t) = 2t, y(t) = t). The curve given as argument to the command is the function f(x) = \( \frac{x²}\{4}\), and the result is the derivative of that function: f'(x) = \( \frac{x}\{2}\).